

A203621


Highly antiimperfect numbers: numbers k that sets a record for the value of sigma*(k)k, where sigma*(k) is the sum of the antidivisors of k.


1



1, 2, 7, 10, 13, 17, 22, 27, 28, 32, 38, 45, 52, 60, 63, 67, 77, 95, 105, 130, 137, 143, 157, 158, 175, 193, 203, 247, 297, 315, 357, 423, 462, 472, 473, 578, 675, 682, 742, 770, 787, 1012, 1138, 1215, 1417, 1463, 1732, 1957, 2047, 2048, 2327, 2363, 2632
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OFFSET

1,2


COMMENTS

Antiimperfect numbers are antideficient numbers or antiabundant numbers.


LINKS



EXAMPLE

n=1. Antidivisors: 0. 01=1
n=2. Antidivisors: 0. 02=2
n=3. Antidivisors: 2. 23=1 less than 2: 3 is not in the sequence.
n=4. Antidivisors: 3. 34=1 less than 2: 4 is not in the sequence.
n=5. Antidivisors: 2,3. 53=2 equal to the maximum: 5 is not in the sequence.
n=6. Antidivisors: 4. 46=2 equal to the maximum: 6 is not in the sequence.
n=7. Antidivisors: 2,3,5. 107=3 new maximum: 7 is in the sequence.


MAPLE

P:=proc(i)
local a, k, n, s;
s:=0;
for n from 1 to i do
a:=0;
for k from 2 to n1 do if abs((n mod k) k/2)<1 then a:=a+k; fi; od;
if abs(na)>s then s:=abs(na); print(n); fi;
od;
end:
P(3000);


MATHEMATICA

sig[n_] := Total[Cases[Range[2, n  1], _?(Abs[Mod[n, #]  #/2] < 1 &)]]; d[n_] := Abs[sig[n]  n]; s = {}; dm = 1; Do[If[(d1 = d[n]) > dm, dm = d1; AppendTo[s, n]], {n, 1, 2700}]; s (* Amiram Eldar, Jan 13 2022 after Michael De Vlieger at A066417 *)


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



